Problem: Find the distance between the points (6, 1) and (-9, 3). {1} {2} {3} {4} {5} {6} {7} {8} {9} {10} {\llap{-}2} {\llap{-}3} {\llap{-}4} {\llap{-}5} {\llap{-}6} {\llap{-}7} {\llap{-}8} {\llap{-}9} {\llap{-}10} {1} {2} {3} {4} {5} {6} {7} {8} {9} {10} {\llap{-}2} {\llap{-}3} {\llap{-}4} {\llap{-}5} {\llap{-}6} {\llap{-}7} {\llap{-}8} {\llap{-}9} {\llap{-}10} (6, 1) (-9, 3) $15$ $2$
Change in $x$ (-9) 15 Change in $y$ The distance is the length of the hypotenuse of this right triangle. By the Pythagorean Theorem, that length is equal to: $\sqrt{15^2 + 2^2}$ $= \sqrt{229}$